
AMERICAN SOCIETY OF CIVIL ENGINEERS. 

INCORPORATED 1852. 



TRANSACTIONS. 

No ik. — I his Society is not responsible, as a body, for the facts and opinions advanced in any of 
its publications. 



ON THE STRENGTH, ELASTICITY, DUCTILITY AND RESILIENCE 
OF MATERIALS OF MACHINE CONSTRUCTION, 

AND ON VARIOUS HITHERTO UNOBSERVED PHENOMENA, NOTICED DURING EXPERIMENTAL 
RESEARCHES WITH A NEW TESTING MACHINE, FITTED WITH AN AUTOGRAPHIC REGISTRY. 

A paper by Prof. K. H. Thurston, Member of the Society, 
Read February 4, 1874. 



Section I. 

1. Introductory.* — Some months ago, while engaged with the ad- 
vanced classes of the Stevens Institute of Technology, in experimental 
investigations of the resistance of materials, it was found that coefficients 
were given, by various authorities, which neither accorded fully with each 
other or with those then obtained. 

The desirability of determining how far these differences were due to 
errors of observation, and how far to variation in the quality of the mate- 
rials examined, induced the writer to design several machines for the 
purpose of conducting with them a more extended and exact series of 
experiments. The machine for measuring torsional resistance was fur- 
nished with an automatic registry, recording a diagram which is a reliable 
and exact representation of all circumstances attending the distortion and 
fracture of the specimen. No system of personal observation could 
probably be devised which could yield results either as reliable or as pre- 
cise as such a system of autographic registry, and, as no method previ- 
ously in use had given simultaneously, and at every instant during the 
test, the intensity of the distorting force and the magnitude of the coin- 
cident distortion, it was anticipated that the new method of investigation 



* Vide Journal Franklin Institute, 1873. 



might be fruitful of new and, possibly, important results. This expecta- 
tion, as will be seen, has been more than realized. 

2. Description of the Appakatus. — 
The machine, as planned by the writer, 
and as built in the instrument makers' 
workshop, at the Stevens Institute, is 
shown in Fig. 1. This form is that 
with which the investigations to be 
described were made. Since its con- 
struction, in 1872, however, some 
changes and improvements have been 
made in the design to adapt it to general 
work, and new designs have been made 
for special kinds of work, as for wire D j 
mills, railroad shops and bridge build- 
ing. 

Two strong wrenches, C E, B D, are 
carried by the frames A A, A 1 A 1 , and 
depend from axes which are both in the 
same line, but are not connected with 
each other. The arm, B, of one of these wrenches carries a weight, D, at 
its lower end. The other arm, C, is designed to be moved by hand, in 
the smaller machines, and by a gear and pinion, or a worm gear in larger 




FiG.2 




forms of the apparatus. The heads of the 
wrenches are made as shown in Fig. 2, the 
recess, M, being fitted to take the head, on the 
end of the test pieces, which is usually given 
the form shown in Fig. 4. 

Fig. 4 




A guide curve, F, of such form that its ordinates are precisely pro- 
portional to the torsional moments exerted by the weighted arm, B D, 
while moving up an arc to which the corresponding abscissas of the curve 
are proportional, is secured to the frame A A 1 . The pencil holder, J, is 
carried on this arm, B B, and as the latter is forced out of the vertical 
position, the pencil is pushed forward by the guide curve, its movement 



being thus made proportionate to the force which, transmitted through 
the test piece, produces deflection of the weighted arm. This guide line 
is a curve of sines. The other arm, C h\ carries the cylinder, G, upon 
which the paper receiving the record is clamped, and the pencil, •/, makes 
its mark on the table thus provided. This table having a motion, rela- 
tively to the pencil, which is precisely the angular relative motion of the 
two extremities of the tested specimen, the curve described upon the 
paper is always of such form that the ordinate of any point measures the 
amount of the distorting force at a certain instant, while its abscissa 
measures the distortion produced at the same instant. The maximum 
hand, J, is sometimes useful as a check upon the record of maximum 
resistance. 

The convenience of operation, the small cost,* and the portability of 
the machine are hardly less important to the engineer than the accuracy, 
and the extraordinary extent of information obtainable by it. 

3. Method of Operation. — The test piece having been given the 
shape and size which are found best suited for the purposes of the experi- 
ment, and to the capacity of the machine, it is placed in the jaws of the 
two wrenches, each of which takes one of its squared ends, and, a force 
"being applied to the handle, E, the strain thrown upon the specimen is 
transmitted through it to the weighted arm, B D, causing it to swing 
about its axis until the weight exerts a moment of resistance which equili- 
brates the applied force. As the magnitude of the distorting force 
changes, the position of the weight simultaneously changes, and the 
pencil indicates, at each instant, the value of the stress upon the test- 
piece. As the piece yields under strains of increasing amount, also, the 
pencil is carried in the direction of the circumference of the cylinder on 
which its record is made, and to a distance which is proportional to the 
amount of distortion, i.e., to the "total angle of torsion." As the ap- 
plied force increases, the specimen yields, and finally, rupture occurring, 
the pencil returns to the base line, at a distance from the starting point 
which measures the angle through which the test piece yielded before its 
fracture became complete. 

±. Interpretation of the Diagrams. — It has been shown that the 
vertical scale of the diagrams produced is a scale of torsional moments, 
and that the horizontal scale is one of total angles of torsion. Since the 
resistance to shearing, in a homogeneous material, varies with the resist- 



; hines of the size of that user! in these experiments, but of improved design, are made 
Stevens Institute, at prices as low as (150. 



ance to longitudinal stress, it follows that the vertical scale is also, for 
such materials, a scale of direct resistance, and that, with approximately 
homogeneous substances, this scale is approximately accurate, where, as 
here, all specimens compared are of the same dimensions. Since the 
elasticity of the material is measured by the ratio of the distorting force, 
to the degree of temporary distortion produced, the diagrams obtained 
will exhibit the elastic properties of the material, as well as measure its 
ductility and its resilience. 

Referring to the diagrams shown in the accompanying plates, it will 
be noticed that the first portion of the hue is a curve of small radius, 
convex toward the axis of abscissas, and that the line then rises at a 
slight inclination from the vertical, but becoming very nearly straight, 
until, at a point some distance above the origin, it takes a reversed curva- 
ture. The first portion of the line is probably formed by the yielding of 
the loosely fitted packing pieces seeming the heads of the specimen, and, 
after they have taken a bearing, by the early yielding, in some materials, 
of particles already overstrained. When a firm hold is obtained, the- 
line becomes sometimes nearly straight, and the amount of distortion is- 
seen to be approximately proportional to the distorting force, illustrating- 
" Hooke's law," Ut tensis sic vis. 

A.ter a degree of distortion which is determined by the specific char- 
acter of each piece, the line becomes curved, the change of form having 
a rate of increase which varies more rapidly than the applied force. 
When this change commences, it seems probable that the molecules, 
which, up to that point, retain generally, their original distribution, while 
varying their relative distances, begin to change their positions with 
respect to each other, moving upon each other in a manner similar, 
probably, to that action described by Mon. Tresca, and called the ' ' Flow 
of Solids," * and to which attention has already been called by Prof. J. 
Thompson, f 

It is this point, at which the line commences to become concave 
toward the base, that is consumed to mark the "limit of elasticity." 
It will be noticed that it is well denned in experiments upon woods, is 
less marked, but still well defined in the "fibrous" irons and the less 
homogeneous specimens of other metals, and becomes quite indetermin- 
able with the most homogeneous materials, as with the best qualities of 
well worked cast-steel. This point does not indicate the first "set," 



* L'Ecoulement des Corps SoJides; Paris, 1869, 1871. 

t Cambridge and Dublin Mathematical Journal, Vol. Ill, 1848, pp. 252-266. 



since, as will be hereafter Been, a set is found to occur, either temporary 
or permanent, and usually partly temporary and partly permanent, with 
every degree of distortion, however small. It is at this "elastic limit" 
that the sots begin to become considerable in amount and almost wholly 
permanent. 

The inclination of the straight portion of the line from the vortical 

measures the stiffness of the specimen, the quantity Cot. O = — -being 

Tan. (y 

the ratio of the distorting force to the amount of distortion up to the 
•• limit of elasticity." As it would seem from the results of experiment, 
as well as of deduction, that this rigidity is very closely, if not precisely, 
proportional to the hardness, in homogeneous substances, this quantity 
Cot. S may be taken, for practical purposes, as a measure of the hardness 
of the metals, as well as of their elastic resistance to compression. 

After passing the elastic limit, the line becomes more and more nearly 
parallel to the base line, and then, with the woods invariably, and in some 
<?ases with the metals, begins to fall rapidly before fracture becomes 
evident in the specimen. Where the rising portion of the line turns and 
becomes nearly parallel with the axis of abscissas, the viscosity of the 
material is such that the outer particles "flow" upon those within, and, 
while themselves still offering maximum resistance, permit molecules 
nearer the axis to also resist with approximately maximum force. It 
seems probable that, with the more ductile substances, nearly all are 
brought up to a maximum in resistance before fracture occurs, and this 
circumstance will be seen hereafter to have an important influence in 
determining the resistance to rupture. The hardest and most brittle 
materials break, with a snap, before any such flow becomes perceivable, 
and before the line of the diagram commences to deviate, in the slightest 
degree, from the direction taken at the beginning, and before the ap- 
proach to the elastic limit is indicated. It is evident that the standard 
formulas for torsional, as well as for other forms of resistance, cannot be 
perfectly correct, since they do not exhibit this difference in the character 
of the resistance offered by ductile and by rigid materials. 

The elasticity of the material is determined by relaxing the distorting 
force, at intervals, and allowing the specimen to relieve itself from dis- 
tortion so far as its elasticity will permit. In such cases, the pencil will 
be found to have traced a line resembling, in its general form and posi- 
tion, in respect to the coordinates, that forming the initial portion of 
the diagram, but almost absolutely straight, and more nearly vertical. 



6 

The degree of inclination of this line indicated the elasticity, precisely as 
the initial straight line was made to give a measure of the original stiff- 
ness of the test piece, the cotangent of the angle made with the vertical, 

Cot. $ = being the ratio of the force required to spring the piece 

Tan. $ 

through the range recoverable by elasticity, to the magnitude of that 

range. The fact, to be shown, that this value is always greater than 

Cot. &, for the same metal is evidence that more or less permanent set 

will always occur, and that the original stiffness of the specimen is always 

modified, whatever the magnitude of the applied force. The form of the 

line of elastic change indicates also the character of the molecular action 

producing it. 

Finally, the form of the curve after passing the maximum, or after 
passing the point at which fracture commences, exhibits the method of 
variation of strength during the process of fracture. This portion is very 
difficult to obtain, with even approximate accuracy, with any but the 
toughest and most ductile materials. This terminal portion of the dia- 
gram would be, theoretically, a cubic parabola, the loss of resisting power 
varying with the progressive rupture of concentric layers, and the re- 
maining unbroken cylindrical portion becoming smaller and smaller until 
resistance vanishes with the fracture of the axial line. In some cases, 
the curves obtained from ductile metals exhibit this parabolic line very 
distinctly. In all hard materials, the jar produced by the sudden rup- 
ture of surface particles is sufficient to separate those within, and the 
terminal line is straight and vertical. 

The homogeneity of the material tested is frequently hardly less im- 
portant than its strength, and it is very desirable to obtain evidence 
which may enable the experimenter to determine the value of tests of 
samples as indicative of the character of the lot from which the specimens 
may have been taken. If the specimens are found to be perfectly homo- 
geneous, it may be assumed with confidence that they represent accu- 
rately the whole lot. If the samples are irregular in structure and in 
strength, no reliable judgment of the value of the lot can be based upon 
their character, and there can be no assurance that, among the pieces 
accepted, there may not be untrustworthy material which may possibly 
be placed just where it is most important to have the best. It is evident 
that the more homegeneous a material, the more regularly would changes 
in its resistance take place, and the smoother and more symmetrical 
would be the diagram. The depression of the line immediately after 



passing the elastic limit exhibits the greater or less homogeneousness of 
the material The fact is illustrated in a striking manner in some of the 
onrves presented, and we thus have — what had never, I believe, been be- 
fore found — this method of determining homogeneousness. 

Tln> -est of the specimen is measured by the area included 

within its curve, this being the product of the mean force exerted into 
tin 1 distance through which it acts in producing rupture, i.e., it is propor- 
tional to the work done by the test piece in resisting fracture, and re- 
presents the value of the material for resisting shock. The area taken 
within the ordinate of the limit of elasticity, measures the capacity for 
resisting shock without serious distortion or injurious set. 

The ductility of the specimen is deduced from the value of the total 
angle of torsion, aud the measure is the elongation of a line of surface 
particles, originally parallel to the axis, which line assumes a helical form 
as the test piece yields, and fiually parts at or near the poiut where the 
maximum resistance is formed. Its value is given on Plates H and III 
for each ten degrees of arc. Since, in this case, there is no appreciable 
reduction of section, or change of form, in the specimen, this value of 
elongation is our actual measure of the maximum ductility of the material, 
and is an even more accurate indication than the area of fractured cross 
section as usually measured after rupture by tension. It is to be under- 
stood that wherever comparisons are here made, without the express 
statement of other conditions, that specimens of the same dimensions 
are always represented in the diagrams. 

5. Description of Illustrated Diagrams. The Woods. — Plates I 
and II exhibit sets of curves which illustrate the general characteristics 
of a large number of materials, the first showing the peculiarities noted 
during experiments on the woods, and the second giving an interesting 
comparison of the metals. 

The woods experimented upon were the following, the numbers of 
the respective curves on Plate I, indicating the material here correspond- 
ingly marked : — 

1. White pine (Pinus Slrobus). 

2. Southern pine (Pinus Australis), sap wood. 

3. Southern pine, heartwood. 
■i. Black spruce (Abies Nigra). 

5. Ash (Fraxinus Americanus). 

6. Black walnut (Juglans Nigra). 

7. Bed cedar (Juniperus Virginianus). 



8 

8. Spanish, mahogany (Swietenia Mahogani). 

9. White oak (Quercus Alba). 

10. Hickory (Gary a Alba). 

11. Locust (Robinia Pseudo-acacia). 

12. Chestnut ( Castanea Vesca). 

The specimens were all of the form shown in Fig. 3, three and 
three-fourths inches long, with a diameter of neck of seven-eighths of 
an inch. 

It will be noticed that, in all cases, at the commencement of the line, 
it rises, at a slight inclination from the vertical, and almost perfectly 
straight. This confirmation of Hooke's law, within the limit of elas- 
ticity, is best shown in the detached portion a, a, a, of the curve ob- 
tained with locust, in which the horizontal scale is somewhat magnified. 
The distortion is seen to be very precisely proportional to the distorting- 
force, until the law changes at the limit of elasticity. 

It will be observed that, in the larger number of cases, the torsional 
resistance increases with great regularity nearly to the angle of maximum 
stress where, suddenly, this rapid rate of increase ceases, and the limit 
of elastic resistance being passed, resistance diminishes rapidly with 
further increase of angular movement, until it becomes zero. In the 
tougher and more dense varieties, this decrease of resistance occurs less 
slowly, and in some cases only disappears after a large angle of torsion 
is recorded. In the curves of exceptionally strong and tough woods, 
in which there is known to exist a great excess of longitudinal over 
lateral cohesion, as in those of black walnut 6, 6, locust 11, 11, and espe- 
cially in those of hickory 10, 10, a peculiarity is perceivable which is 
somewhat remarkable, and which is especially important in a connection 
to be hereafter referred to at length. 

In these instances the resistance is proportional to the amount of 
torsion, until a maximum is reached, the line then falls as torsion con- 
tinues, until a minimum is rmssed, the curve then again rising and pass- 
ing another maximum before finally commencing an unintermitted 
descent to the axis of abscissas. "Where the difference between longi- 
tudinal and lateral cohesion is exceptionally great, the second maximum 
may, as illustrated, for example, by the line described in recording the 
test of hickory, have a higher value even than the first. This interest- 
ing and previously unanticipated peculiarity was shown, by careful 
observation, to be due to the sudden yielding of lateral cohesion when 
the torsional moment reached the value indicated by the first minimum. 



9 

The fibres being thus loosened from each other, this loose bundle of 
filaments yielded readily, until, by lateral crowding as they assumed a 
helical form and enwrapped each oilier, their slipping upon each other 
was gradually checked, and resistance again commenced Increasing. 

At the second maximum, yielding again began in consequence of the 
breaking of fibres under the longitudinal stress measured by that com- 
ponent of torsional force having a direction parallel with the filaments in 
their new positions, the exterior surface threads parting first under this 
tensile stress, and rupture progressing by the yielding of layer after 
layer, until the axial line being reached, resistance vanished. In this 
ease, rupture seems never to occur by true shearing along one defined 
transverse plane. This feature of depression in the curve, occurring as 
described, is therefore the indication of a lack of symmetry in the dis- 
tribution of resisting forces. It is evident that it may occur either by 
a difference in the value of cohesive force in the lateral and longitudinal 
directions, or by the structural defects of a specimen in which the sub- 
stance itself may be endowed with cohesion of equal intensity in all 
directions. 

The curves shown in Plate I exhibit well the relative values of these 
materials for the various purposes of the engineer. 

White pine, 1, 1, 1, is shown by the considerable inclination of the 
line of stiffness from the vertical, to be soft and deficient in rigidity. 
The limit of elasticity is quickly reached, and the maximum resistance of 
the specimen is found at 151- foot-pounds of moment. Rapidly losing 
strength after passing the limit of resistance, it is entirely broken off 
at an angle of 130°. The small area comprised by the diagram proves 
its deficiency of resistance, and its inability to sustain shock. 

Yellow pine, 2, 2, 2, 3, 3, 3, far excels the first in all valuable prop- 
erties shown by the curve. The sapwood seems, in the specimens tested, 
equally stiff with the heart, but it reaches the elastic limit sooner. The 
general form of the diagram is the same in both, and is characteristically 
different from that of the white pine. It evidently has great value wher- 
ever rigidity, strength, toughness and resilience are desired in combina- 
tion with lightness, the latter most important quality, together with, their 
cheapness, aiding the qualities here shown in determining the applica- 
tion of these woods so extensively for general purposes. It should be 
noted that, since all comparisons of strength are based on measures of 
volume, a comparison of densities should usually be obtained to assist 
the judgment in making a choice from among materials of which tests 
have been made. 



10 

Spruce, 4, 4. 4, while possessing far less stiffness than even white 
pine, excels it somewhat in strength, passing its maximum at 18 foot- 
pounds, and submitting to a torsion of nearly 200 z . It is proven to 
possess, proportionally greater resilience also. It is, however, far in- 
ferior to the yellow pine in every respect. 

Ash, 5, 5, 5, is more deficient in strength and toughness than is gen- 
erally supposed, and rapidly loses its power of resistance after passing 
the maximum, which rjoint is found at about 27| foot-pounds. These 
specimens may have been of exceptionally poor quality, or, possibly, were 
over-seasoned. 

Black walnut, 6, 6, 6, is remarkably stiff, strong and resilient, its dia- 
gram resembling somewhat that of oak in general form and dimensions. 
The maximum of resistance reaches 35 foot-pounds, and the most ductile 
specimen was only broken off after yielding through an arc of 220°. Its 
stiffness is shown by the fact that it required a moment of 25 foot-pounds 
to spring it 10", yellow pine requiring but 22 foot-pounds and spruce but 
8, to give them the same amount of distortion. 

Eed cedar, 7, 7, 7, is very stiff, but is brittle and deficient in strength,, 
breaking off at 92-, and having a maximum power of resistance of 
but 20V- foot-pounds. It is, however, one of the stiffest of the woods, 
its specimen requiring 20 footpounds of torsional moment to produce a 
total angle of torsion of but 5 : . 

Spanish mahogany, 8, 8, 8, is both strong and stiff, bearing a stress 
of 44 foot-pounds, and requiring 32 to produce torsion of 10°. 

White oak, 9, 9, 9, exhibits less strength than either good mahogany, 
locust or hickory, but it is exceedingly tough and resilient. Passing the 
maximum at an angle of 15°, under a torsional stress of 35V foot-pounds, 
it retains its power of resistance nearly unimpaired up to about 70°, and 
then slowly yields until it suddenly gives way, after passing the angle 
250°, under a strain due to 9 foot-pounds, and breaks off completely at 
253 : . This strength, toughness and endurance, under strains due to im- 
pact, may be attributed to its considerable lateral cohesion, and to the 
interlacing of its tenacious fibres, which gives this wood its "cross"" 
grain. 

Hickory, 10, 10, 10, has the highest maximum found during these ex- 
periments, the second of the pair of maxima already referred to being 
considerably above the maximum of locust even. This specimen exhibits 
well the well-known valuable properties of the material, requiring 45 
foot-pounds to twist it 10 : , reaching a limit of elasticity at 54 foot- 



11 

pounds and 13 . and faring a maximum resisting moment of 594 foot- 
pounds. When it final! v yields, it does so quite rapidly, breaking off at 

Locust. 11. 11. 11. gives an excellent diagram. It is the stiffest of alL 
yielding bat 1«> at its maximum of 55 foot-pounds, and one piece, which 
was unusually hard and compact, requiring 48 foot-pounds to distort it 
1 reaching a maximum angle of torsion of nearly 1 
It was noticed, during this series of experiments, that different spe- 
cimens of the sune species of wood usually exhibited Terr nearly equal 
<z ---__-l. jli. : ::_•: I'-. . •_ '. :"_:.: i_ :.:1- : 'Izi-z-z. :-f- — -rr-r ;-_'.- . :.-: _..!- 
noted in elasticity and resilience. 

6. The Metals, axd the Cteves pbotht zz it mm — II be II exr 
!:•::;>:--• : v.- -- —"_: I II >:: :- — rl "I . rri.fr.1 "_ : :_::-:_- 
and the peculiarities of representative specimens of the principal 
Tiri-ri— : ". — : I i_t: I- Iz. - :_r : — - :~ -- t :_t_- I .-- ':_—- 
■- --. .. : — !::■! :z -It-tz:-:! :.- t :/_. _■■ _li~ — lilr 
:Ir :!:>:! -: zl z_ ' I : " :: rriszz : ii.= 

The diagrams obtained by testing metals are quite different in general 
_ -'_. - : _.-:.-'. :z r— TrJz.ri:- :z '.'_- — ' • -■■.-.'..-:- 



: 

-;z :- :"_r>r - 



zi-tz 



by a eomparatirel 

zz _ zs : f: ~ z L^t t 

:Iit.. I- I ..~__ "I : 

: -: 71: l-:I 



and thoroughly annealed cast-steel, as an example, is equally strong 
all directions, is perfectly uniform in its structural character, and 
almost absolutely homogeneous as to strain. It would be expected, thei 
fore, that the diagrams obtained by breaking such a mafa»ria1 would d£B 
from those of the woods, in having a smoother and more regular f on 
and this is shown to be actuallr the case bv observation of the c 



12 

cast-steel, cast-iron, bronze and others of the more homogeneous metals 
and alloys. 

Some of the metals, it will be noticed, yield diagrams of less regular 
form. Wrought-iron, as usually made, has a somewhat fibrous structure, 
which is produced by particles of cinder, originally left in the mass by 
the imperfect work of the puddler while forming the ball of sponge in 
his furnace, and which, not having been removed by the squeezers or by 
hammering the puddle ball, are, by the subsequent process of rolling, 
drawn out into long lines of non-cohering matter, and produce an effect 
upon the mass of metal which makes its behavior, under stress, some- 
what similar to that of the stronger and more thready kinds of wood. 
In the low steels, also, in which, in consequence of the deficiency of 
manganese accompanying, almost of necessity, their low proportion of 
carbon, this fibrous structure is produced by cells and "bubble holes " in 
ihe ingot, refusing to weld up in working, and drawing out into long 
microscopic, or less than microscopic, capillary openings. 

In consequence of this structure we find, as we should have antici- 
pated, a depression interrupting the regularity of their curves, imme- 
diately after passing the limit of elasticity, precisely as the same indica- 
tion of the lack of homogeneousness of structure was seen in the diagrams 
produced by locust and hickory. 

The presence of internal strain constitutes an essential peculiarity of 
the metals which distinguishes them from organic materials. The latter 
are built up by the action of molecular forces, and their j>articles assume 
naturally, and probably invariably, positions of equilibrium as to strain. 
The same is true of naturally formed organic substances. The metals, 
however, are given form by external and artificially produced forces. 
Their molecules are compelled to assume certain relative positions, and 
those positions may be those of equilibrium, or they may be such as to 
strain the cohesive forces to the very limit of their reach. It even frequent- 
ly happens, in large masses, that these internal strains actually result in 
rupture of portions of the material at various points, while in other places 
the particles are either strongly compressed, or are on the verge of com- 
plete separation by tension. This peculiar condition must evidently be of 
serious importance, where the metal is brittle, as is illustrated by the 
behavior of cast-iron, and particularly in ordnance. Even in ductile 
metals it must evidently produce a reduction in the power of the mate- 
rial to resist external forees. This condition of internal strain may be 
relieved by annealing hammered and rolled metals, and by cooling cast- 



13 

fugs vcr\ slowly, in order thai 1 lu* particles may assume, naturally, po- 
sitions d\' equilibrium. In tough and ductile metals, internal strain may 
be removed by heating to a high temperature and then cooling under 
tin* action of a force approximately equal to the clastic resistance of the 
substance. This process, called " Thermo-tension, " was first used by 
Professor Johnson in the course of his experiments as a member of a 
Committee of the Franklin Institute, in 1836,* and the effect of this 
action in apparently strengthening the bars so treated, was stated in the 
report of the committee. The fact that this effect was very different 
with different kinds of iron was also noted, but it does not appear that 
the cause of this, which they term "an anomalous " condition of the 
metal was discovered by them. 

Metals which are very ductile may frequently be relieved of internal 
strain, also, by simply straining them while cold to the elastic limit, and 
thus dragging all their particles into extreme positions of tension, from 
which, when released from strain, they may all spring back into 
their natural and unstrained positions of equilibrium. This fact, which 
does not seem to have been previously discovered by investigators of 
this subject, will be seen to have an important bearing upon the resist- 
ing power of materials, and upon the character of all formulas in which 
it may be attempted to embody accurately the law of resistance of such, 
materials to distorting or breaking strain. 

Since straining the piece to the limit of elasticity brings all particles 
subject to this internal strain into a similar condition, as to strain, with 
adjacent particles, it is evident that indications of the existence of in- 
ternal strain, and through such indications a knowledge of. the value of 
the specimen, as affected by this condition, must be sought in the 
diagram, before the sharp change of direction which usually marks the 
position of the limit of elasticity is reached. As already seen, the initial 
portion of the diagram, when the material is free from internal strain, is 
a straight line up to the limit of elasticity. A careful observation of the 
tests of materials of various qualities, while under test, has shown that, 
as would, from considerations to be stated more fully hereafter, in treat- 
ing of the theory of rupture, be expected, this line, with strained mate- 
rials, becomes convex towards the base line, and the form of the curve, 
as will be shown, is parabolic. The initial portion of the diagram, there- 
fore, determines readily whether the material tested has been subjected 

* Journal Franklin Institute, 1836--7. 



14 

to internal strain, or whether it is homogeneous as to strain. This is ex- 
hibited by the direction of this part of the line as well as by its form. 
The existence of internal strain causes a loss of stiffness, which is shown 
by the deviation of this part of the line from the vertical to a degree 
which becomes observable by comparing its inclination with that of the 
line of elastic resistance, obtained by relaxing the distorting force — i. e. , 
the difference in inclination of the initial line of the diagram and the 
lines of elastic resistance, e, e, e, indicates the amount of existing in- 
ternal strains. 

7. Forged Iron. — In Plate II, the curves numbered 6, 1, 22 and 100, 
are the diagrams produced by three characteristic grades of wrought- 
iron. The first is a quality of English iron, well known in our market 
a,s a superior metal. The second is one of the finest known brands of 
American iron, and the third is also of American make, but it does not 
usually come into the market in competition with well known irons, in 
consequence of the high price which is consequent upon the necessary 
employment of an unusual amount of labor, in securing its extraordina- 
rily high character. 

No. 6 at first yields rapidly under moderate force, only about 50 
foot-pounds of torsional moment being required to twist it 5°. It 
then rapidly becomes more rigid, as the internal strains, so plainly 
indicated, are lost in this change of form, and at 6° of torsion, the 
resistance becomes 60 foot-pounds, as measured at a. Here the elastic 
limit is reached. The next 3° produce no increase of resistance. 
This fact shows that this iron, which was not homogeneous as to 
strain, is also not homogeneous in structure. We conclude that it must 
be badly worked and seamy, and that it may have been rolled too cold ; 
the former is the probable reason of its lack of homogeneous struc- 
ture, the latter gave it its condition of internal strain. After the first 
9° of torsion, resistance steadily rises to a maximum, which is 
reached only when just on the point of rupture, and the piece finally 
commences breaking at 250°, and is entirely broken off at 285°. 
Its maximum elongation, whose value is proportionable to the reduction 
of section noted with the standard testing machines, is 0.691. The 
terminal portion of the line, after rupture commences, is not usually 
accurate as a measure of the relation of the force to the distortion. The 
increase of resistance between the angle 9° and the angle of rupture is 
produced by the additional effort in resistance due to the "flow" or 
drawing out of particles, as already indicated, and the precise effect of 



15 

which "will be noticed at Length in ;i succeeding section relating to the 
theory of rupture. 

Applying the scale tor tension, which in the case of these curves whs 
very exactly -J 1.000 pounds per square inch for each inch measured ver- 
tically on the diagram, we find that the elastic limit was passed under a 
stress equivalent to a tension of 19,800 pounds per square inch, and that 
the ultimate tenacity was 50,200 pounds per square inch. When nearly 
at the maximum the specimen was relieved from stress, the pencil de- 
scending to the base line, and the elasticity of the piece produced a cer- 
tain amount of recoil. The angle intercepted between the foot of this 
nearly vertical line, c, and the origin at o, measures the set, which is al- 
most entirely permanent. The distance measured from the foot of the 
perpendicular, let fall upon the axis of abscissas, from the head of this 
line to the foot of the line e, measures the elasticity, and is inversely pro- 
portional to the modulus. A comparison of the inclination of the line 
made by the pencil in reascending, on the renewal of the strain with the 
initial line of the diagram, gives the indication of the amount of internal 
strain originally existing in the piece. 

It will be noticed that the horizontal movement of the pencil is re- 
commenced at /, under a higher resistance than w r as recorded before the 
elastic line was formed. In this case the piece had been left under strain 
for some time before the stress was relieved, and the peculiarity noted is 
an example of an increase of resistance under stress,* or more properly 
of the elevation of the elastic limit, of which more marked examples will be 
shown subsequently. 

The exceptional stiffness and limited elastic range here showm, as 
compared with the other examples given, is probably a phenomenon ac- 
companying and due to this increase of resistance under stress. 

Examining No. 1 in a similar manner, we find that it is far freer from 
internal strain than No. 6, its initial line being much more nearly 
straight and rising more rapidly. It is rather less homogeneous in 
structure, and is forced through an arc of 6°, after having passed its 
elastic limit, before it begins to offer an increasing resistance. It is 
evidently a better iron, but less well worked, and, as showm by the posi- 
tion of the elastic limit, is somewdiat harder and stiffer. No. 1 retains 
its higher resistance quite up to the point at wdiich No. 6 received its in- 
cidental accession of resistance by standing under strain, and the two 
pieces break at, practically, the same point, No. 1 having slightly the 

* Vide Transactions, Vol. II, page 290. 



16 

greater ductility. When the " elastic line," <?, is formed, just before frac- 
ture, it is seen that Xo. 1 has a greater elastic range and a lower modulus 
than Xo. 5. It should be observed that the line by which the pencil 
descends to the base line has usually no value, owing to the fact that no 
care is generally taken to remove the stress as gradually as it is applied. 
When such care is taken, the lines are usually coincident, and do not 
form the loop here seen. It will also be noticed that these lines often 
cross each other, that on the right being the important line. The elastic 
line formed by Xo. 1 at between 40 : and 45° of torsion is seen to be very 
nearly parallel with that obtained near the terminal portion of the 
diagram, and illustrates the fact here first revealed to the eye, that tiie 
elasticity of the specimen remains practically unchanged up to the point of 
incipient rupture, and this fact corroborates the deductions of TVertheini* 
and others who came to this conclusion from less satisfactory modes of 
research. All experiments yet made give a similar result. 

Xo. 22 illustrates the characteristics of a metal which probably re- 
presents one of the best qualities of wrought iron made in this or in any 
other countiy, and with which every precaution has been taken to secure 
the greatest possible perfection, both in the raw material and in its manu- 
facture. The fact that it finds a market at sixteen cents a pound 
proves that even such care and expense are well applied. The line of 
this diagram, starting from 0, rising with hardly perceptible variation 
from its general direction, turns, at the elastic limit, a, under a moment 
of about 80 foot-pounds, equivalent to a tension of about 24,000 
pounds per square inch ; and with between 2° and 3 C of torsion only, 
and thence continues rising in a curve almost as smooth and regular as if 
it had been constructed by a skilful draughtsman. Reaching a maximum 
of resistance to torsion of 220 foot-pounds and an equivalent tensile resist- 
ance of over 66,000 pounds per square inch, at an angle of 345°, it retains 
this high resistance up to the point of rupture some 358- from its starting 
point. The maximum elongation of its exterior fibres is 1. 2, making them 
at rupture 2.2 times their original length. This would produce a probable 
breaking section in the common testing machine equal to 0.4545 of the 
original section, f 

From the beginning to the end this specimen exhibits its superiority, 
in all respects, over the less carefully made irons, Xos. 1 and 6, which, it 
should be remembered, are themselves deservedly known as good brands. 

* Vide Annals de Chimie et de Physique. 

t Compare Kirkaldy ; Strength of Iron and Steel: pp. Ill, 135, for reduction in Yorkshire 
and Swedish oars. The elongation there given has, of course, no value as a measure of 
ductility. 



17 

The homogeneous] ss N 22 is almost perfect, both in regard to strain 
and to structnre, the former being indicated by the straightnesa of the 
first part of the diagram and its parallelism with the " elastic In 
produced at 217. . and the latter being proven by the beautiful accuracy 
with which the curve follows the parabolic path indicated by our th< ory 
as that which should be produced by a ductile homogeneous material. 
At similar angles of torsion, No. 22 offers invariably much higher resistance 
than either Nos. 1 or 6, and this superiority, uniting with its much greater 
ductility, indicates an immensely greater resilience. It is evident that 
for many cases, where lightness combined with capacity to carry live 
loads and to resist heavy shocks are the essential requisites, this iron 
would be by far preferable, notwithstanding the cost of its manufacture, 
to any of the cheaper grades. Comparing their elasticities, as shown at 
1210 . 215°, it is seen that Xo. 22 is about equally stiff and elastic with No. 
1, while both have a wider elastic range and are less rigid, and hence 
are softer than Xo. 6, whose elastic line is seen at 221°. All of the 
characteristics here noted can be accurately gauged by measuring the 
diagrams, and constants are readily obtained for all formulas, as illus- 
trated in a later section of this paper, in which the construction of 
formulas and the determination of constants will be made the subject of 
investigation. 

Xo. 100 is the curve obtained from a piece of Swedish iron, marked 
/<Q^\ • Its characteristics are so well marked that one familiar with the 
^5j£/ nietal would hardly fail to select this curve from among those of other 
irons. Its softness and its homogeneous structure are its pecuharities. Its 
curve, at first, coincides perfectly with that of Xo. 6. It has, however, 
slightly less of the condition of internal strain, and a somewhat higher 
limit of elasticity. The elastic limit is found at 5£° of torsion, and at a 
stress of 65 foot-pounds of moment, equivalent to 19,500 pounds on the 
square inch, in tension. Its increase of resistance, as successive layers are 
brought to their maximum and begin to flow, is very nearly the same as 
that of the specimens Xos. 1 and 6, and the line lies between the diagrams 
given by these irons up to 30-, and then falls slightly below the latter. 
At 220° . it attains a maximum resisting power, and here the outer surface 
begins to rupture, after an ultimate stretch, of lines formerly parallel to 
the axis, amounting to 0.561. Had this elongation taken place in the 
direction of strain, as in the usual form of testing machine, it would 
have produced a reduction of section to 0.61, the original area.* At this 

♦Compare Styffe; Strength of Iron and Steel; p. 133, Nos. 26-30. 



18 



point the stress in tension equivalent to the 176 foot-pounds of torsional 
stress, is 52,800 pounds per square inch. From 250° the loss of resist- 
ance takes place rapidly, but the actual breaking off of the specimen did 
not occur until it had been given a complete revolution. This part of 
the diagram distinguishes the metal from all others, and shows distinctly 
the exceptionally tough, ductile and homogeneous character which gives 
the Swedish irons their superiority in steel making. No. 22, even, 
although much more more extensible, is harder than No. 100, and yields 
more suddenly when it finally gives way. 

A comparison of the results here recorded with those obtained by 
Styffe,* will afford a good basis upon which to form an idea of the ac- 
curacy as well as the convenience of this method of deriving them. An 
examination of the broken test piece gives some evidence confirmatory 
of the record. The exterior surface of the twisted portion has an appear- 
ance intermediate between that of No. 1, Fig. 5,f and No. 22, Fig. 7, with 
an evident tendency to "kink." The surface of fracture is lighter and 
more lead-like than even No. 22, and its "fibre " is finer and texture more 
plastic in appearance. It is beautifully uniform in character. On one 
end of this specimen, where a piece had been nicked and then broken off 
l)y a sharp blow, the absence of all fibrous appearance, and the granular 
texture and magnificently fine, regular grain are Fig. 5. 

very marked, and indicate that the material is 
entitled to its established position as the purest 
Fig. 6. metal known in the 

market. The speci- 
mens themselves fur- 
nish almost as valuable 
information, after test, 
as the diagrams con- 
tain, and should al- 
ways be carefully in- 
3§§jg spected with a view to 

{HI securing additional or corroborative informa- 
: Ijjption. Fig. 5 is a sketch of specimen No. 1, 
ijrzr " and shows its somewhat granular fracture, and 
the seamy structure produced by a defective 
method of working. Fig. 6, from specimen No. 16, more nearly resembles 

* As on last page. 

t From an article in the Scientific American, of January 17th, 1874, on " Testing the Qualitj 
of Iron, Steel and other Metals without Special Apparatus." 





19 




that which gave the diagram marked 6. The metal La Been to be g lod, 
tough, and better in quality than No. 1. but it is even more seamy, and 
even less thoroughly worked, as is evidenced by the cracks extending 
around the neck, and by the irregularly distributed flaws seen on its end. 

Pig. 7 exhibits the appearance of No. Fig- <• 

'22 after fracture, and shows, even more 
perfectly than the penciled record, the 
splendid character of the material. The 
surface of the neck was originally smoothly 
turned and polished, and carefully fitted to 
gauge. Under test it has become curiously 
altered, and has assumed a rough, striated 
appearance, while the helical markings ex- 
tend completely around it. The end has 
the peculiar appearance which will be seen 
to be characteristic of tough and ductile 
metals, and the uniformly bright appear- 
ance of every particle in the fractured section shows how all held to- 
gether up to the instant of rupture, and that fracture finally took place 
by true shearing. Paipture by torsion thus brings to light every defect 
and reveals every excellence in the specim?n. Rupture by tension rarely 
reveals more than the mere strength of the material. 

8. — Low Steels. — In Plate II, and above the curves just described, 
are a set obtained during experiments on '"low steels," produced by 
the Bessemer and Siemens-Martin processes. In general character, 
the curves are seen to resemble those of the standard irons, as 
illustrated by Xos. 1 and 6. The irons contain usually barely a trace of 
carbon. These steels contain from one-half to five-eighths of one per 
cent. The irons are made by a process which leaves them more or less 
injured by the presence of impurities, from which the utmost care can 
seldom free them. The steels are made from metal which has been 
molten and cast, a process which allows a far more complete separation 
■ low steels. 1 to an objection- 

able amount of porosity, due to the liberation of gas while the molten 
mass is solidifying, whenever the spi 

carbon, is not very rich in m The results of these diffi i 

institution and treatment are read by inspecting the c 

They Bhow a stiffness equal to No. 6, and about the San of in- 

ternal strain. They contain a sufficient num 



20 

produced by drawing down the pores while working the ingot into bar. 
to cause a lack of homogeneousness in structure, very similar to that pro- 
duced in iron by cinder. They hare a much higher elastic limit, and 
greater strength, and the softer grades have great ductility. In resilience, 
these softest steels excel all other metals, except the unusual example. 
No. 22. and are evidently the best materials that are now obtainable 
for all uses where a tough, strong, ductile metal is needed to sustain safely 
heavy shocks. A comparison of the diagrams of two competing metals 
may thus be made to indicate how far a difference in price should act as a 
bar to the use of the costlier one. For many purposes, a metal having 
double the resilience of another is worth more than double-price. For 
general purposes, a comparison of the resilience of the metals within the 
elastic limit is of supreme importance. No. 6 is seeu to have more 
resilience within this limit than No. 1. and the steels far more than 
either ; but Xo. 1 would take a set of considerable amount fai within 
the true elastic limit, as indicated at a. The most valuable measure is 
obtained by determining the area intercepted between the "elastic 
line " and the perpendicular let fall from its upper end ; this measures 
the resilience of elastic resistance, which is the really important quality. 

Xo. 9S was cut from the head of an English Bessemer rail made from 
unmixed Cumberland ores. It contains nearly 0.1 per cent, carbon. It is 
quite homogeneous, has a limit of elasticity at 88 foot-pounds of torsional, 
or 26, 400 pounds per square inch tensile stress, approaches its maximum 
of resistance rapidly, and, at 210 : , the torsional moment becomes 225 foot- 
pounds, equivalent to 67.500 pounds per square inch tensile stress. It 
only breaks after a torsion of 283°, and with an ultimate elongation of 
80 per cent, equivalent to a reduction of cross section to 0.556. 

Xo. 76 is a Siemens-Martin steel made from mixed Lake Superior 
and Iron Mountain ores, and contained about the same amount of carbon 
as the preceding. It contains rather more phosphorus, which probably 
gives it its somewhat greater hardness, its higher limit of elasticity and 
its somewhat reduced ductility. Its elastic limit is found at 104 foot- 
pounds of torsion, or 31,200 pounds tensile resistance, and its ultimate 
strength is almost precisely that of the preceding specimen. Its elongation 
is 0.66 maximum. Unless more seriously affected by extreme cold than 
Xo. 98. it would be preferred for rails, and. perhaps, for most purposes. 

No. 67 is a somewhat "higher*' steel, made by the same process. It is 
less homogeneous than the two just examined, has greater strength and a 
higher elastic limit, but less ductility. Its resilience is very nearlv the 



21 

■me as that of K a. 98 and 76. The elasticity of all of tb 

vrrv exactly the same. The ductility of No. 67 is measured by < ». 1' > elon- 
s seen another illustration of elevation oi the elastic limit. 
The piece was left twenty-four hours under maximum stress. The tor- 
sional force was then removed entirely. On renewing it. as is seen, the 
nee of the specimen was found increased in a marked degree. 

No. > is an American Bessemer steel, containing not far from 0.5 
per cent, carbon. The same effect is seen here that was before noted, an 
increase of hardness, a higher elastic limit, and greater strength, ob- 
tained however, by some sacrifice of both ductility and resilience. The 
elastic limit is approached at 130 foot-pounds of torsional moment, or 
pounds tensile, and the maximum is 280 foot-pounds of moment 
and 84,000 pounds tensile resistance at 133- . Its maximum angle of tor- 
sion is 150°, its elongation 0.24. 

Xo. 85 is a singular illustration of the effects of what is probably a 
peculiar modification of internal strain. It seems to have no character- 
isti - in common with any other metal examined. Its diagram would 
seem to show a perfect honiogeneousness as to strain, and a remarkable 
deficiency of homogeneity in structure. It begins to exhibit the indi- 
cations of an elastic limit at a, under a torsional moment of 110 foot- 
pounds, or an apparent tensile stress of 33,000 pounds per square inch, 
and then rises at once by a beautifully regular curve, to very nearly its 
maximum at 16 : , and 176 foot-pounds. The maximum is finally reached 
at 130 : , and thence the line slowly falls until fracture takes place at 195°. 
The maximum resistance seenis* to be very exactly 60,000 pounds to the 
square inch. Its maximum elongation for exterior fibres is about 0.23. 
The resilience taken at the elastic limit is far higher than with common 
iron, and it is seen that this metal, in many respects, may compete with 
steel. Its elasticity is seen to remain constant wherever taken. This 
singular specimen was a piece of "cold rolled*" iron. It is probably 
really far from homogeneous as to strain, but its artificially produced 
strains are symmetrically distributed about its axis, and being rendered 
perfectly uniform throughout each of the concentric cylinders into which 
it may lie conceived to be divided, the effect, so far as this test, or so far 
u its application as shafting, for example, is concerned, is that of perfect 
homogeneousness. The apparently great deficiency of homogeneousness 
in structure is readily explained by an examination of the pieces after 

* With an exceptional case, of which this is an example, the scale for tension is incorrect. 
The tensile strength is probably higher than here given. 



22 

fracture ; they are fibrous, and have a grain as thread-like as oak ; their 
condition is precisely what is shown by the diagram, and the metal itself 
is as anomalous as its curve. 

8. Toon Steels. — The " tool steels" differ chemically from the "low 
steels" in containing a higher percentage of carbon, and usually, in being 
very nearly, if not absolutely, free from all injurious elements. They 
are made in crucibles by melting down the blister steels which are the 
crude product of the process of cementation, or sometimes, by melting a 
charge composed of selected iron, a small proportion of manganese bear- 
ing alloy and the proper amount of carbon. Containing a higher pro- 
portion of carbon than the preceding class of metals, it is comparatively 
easy to secure hornogeneousness by the introduction of manganese, and 
by the same means, to eliminate very perfectly the evil effects of any 
small proportion of sulphur that may be present. Their comparatively 
large admixture of carbon makes them harder, and reduces their duc- 
tility, and since the reduction of ductility occurs to a greater degree than 
the increase of strength, the effect is also to reduce their resilience. The 
working of these metals is more thorough than is that of the less valuable 
steels, or of iron. They are cast in comparatively small ingots, and are 
frequently drawn down under the hammer, instead of in the rolls, and 
are thus more completely freed from that form of irregularity in struc- 
ture noticed so invariably in steels otherwise treated. The effect of in- 
creasing the proportion of carbon, is to confer upon iron the property of 
hardening, when heated to a high temperature, and suddenly cooling, 
and the invaluable property of "taking a temper," i.e., of assuming, 
under proper treatment, any desired degree of hardness. The hard 
steels are, however, comparatively brittle, the hardening being secured 
at the expense of ductility. The effect produced upon the tenacity of 
unhardened steel, by increasing proportions of carbon is somewhat vari- 
able, since it is influenced greatly by the presence of other elements. 
For good steels unhardened, the writer has been accustomed to estimate 
tenacity by the following formula, which is approximately accurate, and 
may be often found useful 

T= 60,000 + 70,000 C. 
in which T represents the tenacity in pounds per square inch, and G is 
the percentage of carbon contained in the metal. This subject will be 
considered at greater length after a series of experiments have been made 
to obtain more exact determinations. 

Referring to Plate II, a set of diagrams will be found, having their 



23 

origin at I s " . which are/ac similes of those automatically produced 

during experiments Qpon various kinds of tool steels. 

No. ">s is an English metal, known in the market as "German 
crucible steel." It is remarkable as having a condition of internal 
strain which has distorted its diagram to such an extent as to completely 

hide the usual indication of the elastic limit. A careful inspection 
shows what may be taken for this point at about 14V- of torsion, when 
the twisting moment was about 120 foot-pounds, and the tensile resist- 
ance 36,000 pounds per square inch. The metal is homogeneous in 
structure, has an ultimate resistance of 302 foot-pounds of moment, or 
90,600 pounds per square inch tensile resistance. Its resilience is evi- 
dently inferior to that of the softer metals, and also less than the next 
higher and better grades. This metal contains about 0. 60 to 0. 65 per 
cent, carbon. Its elongation amounts to 0.045. 

Xo. 53 is an English "double shear steel." of evidently very ex- 
cellent structure, but less strong and less resilient than the preceding. 
Its exterior fibres are drawn out three per cent. 

Nos. 41 and 61 are two specimens of one of the best English tool steels 
in our market. The first was tested as cut from the bar. but the second 
was carefully annealed before the experiment. In this instance, anneal- 
ing has caused a slight loss of resilience as well as a decided loss of 
strength. In Xo. 41, the limit of elasticity can hardly be detected, but 
seems to be at about the same point as in Xo. 61, at near 130 foot-pounds 
moment and 39,000 pounds tension. The ultimate strength is nearly 
119,000 pounds per square inch. The proportion of carbon is very 
closely 1 per cent. Its section would reduce by tension, 0.05. 

Xo. 70 is an American '-'spring steel," rather hard, but as shown by 
its considerable resilience, of excellent quality, resembling remarkably 
the tool steel Xo. 41. It differs from the latter, apparently by its 
much higher elastic limit. It is possible that this may have been caused 
by more rapidly cooling after leaving the rolls in which it was last 
worked. It is evident that, for exact comparison, all specimens should 
be either equally well annealed or should be tempered in a precisely 
similar manner, and to the same degree. 

Xos. 71 and 82 are American tool steels, containing about 1.15 of 
carbon. The former is notable as having an elastic hmit at 69,000 
pounds, and a probable deficiency of manganese, producing the usual 
indication of heterogeneous structure. Both of these steels lack resi- 
lience, and are less well adapted for tools like cold chisels, rock drills, 



24 



and others which are subjected to blows, than for machine tools. They 
have a maximum elongation, respectively, of but 0.013 and 0.03. 

Interesting and instructive as the study of these curves may be 
made, the information obtained from them is supplemented, in a most 
valuable manner, by that obtained by the inspection of the fractured 
specimens, upon which the peculiar action of a torsional strain has pro- 
duced an effect in revealing the structure and quality of the metal that 
could be obtained in no other way. 

Fig. 8 represents the appearance of No. 68, and Fig. 9 that of No. 
Fig. 8. Fig, 9. 





58, while the peculiarities of the finest tool steels are seen in No. 71, as 
Fig. 10. shown in Fig. 10. The smooth exterior of 

No. 68, which is a companion specimen to that 
giving diagram 69, and its bright and charac- 
teristic fracture, resembling that of No. 22 
somewhat, together indicate its nature per- 
fectly, the first feature proving its strength 
and uniformity of structure, and the second 
jUl showing, even to the inexperienced eye, its 
toughness. This is a representative speci- 
men of low steels. No. 58 is seen to have 
retained, even more than No. 68, its original 
smoothly polished surface. Its fracture is 
less waxy, and much more irregular and sharply angular. The crack 
running down the side of the neck shows its relationship to the shear 
steels which much oftener exhibit this effect of strain, in consequence of 
their lamelkr character. No. 58 is evidently intermediate in its charac- 
ter between the soft steels, like No. 68. an \ the tools steels which are 




1 by No. 71, Pig. 10. In this test-piece, the fracturi 
and splintery, and the separated surfaces have a beautifully fine, even 
grain, which proves the excellence of the material The Burface which 

Lined and polished in bringing the metal to size remains as p 
as before the specimen was broken. By an inspection of the brok< 

- in this manner, the grade of the steel, and such properti - i lso as 
are not revealed by an examination of the diagram of strain, are very 
ined by a novice, and to the practical eye. the slightest 
possible variations of character are readily distinguishable. 

9. Cast-iuox. — The diagrams of strain having their commencement 
at 100 . have been obtained from cast-iron and from malleableized 
cast-iron. 

N< is. 23 and 2± are those given by a good dark grey foundry iron from 
Pennsylvania. Xo. 25 represents the curve of light grey scrap, and Xo. 
from a very fine white Lake Superior charcoal iron. The latter is 
seen to be exceedingly hard and rigid, the resistance of the piece rising 
very precisely in proportion to the angle of torsion until it snaps at last 
under a moment of over 200 foot-pounds, equivalent to a tension of 
60,000 pounds per square inch, and with a maximum elongation of one- 
tenth of one per cent. This is a most extraordinary resistance, but it 
is evident that, notwithstanding its immense strength, this material 
would be valueless for ordinary purposes in consequence of its excessive 
brittlenc--. "When the torsional effort had reached about one-half its 
maximum amount the piece was released. The pencil retreated along a 
nearly vertical line e, which it again traversed as the strain was gradually 
renewed. Here as in many other cases, where a similar experiment was 
made, evidence is given of the truth of the statement originally made by 
Hodgkinson.^" that every load produces a set. As will be shown, sub- 
sequently, however, it is not true in perfectly homogeneous bodies free 
from strain, and within their elastic limit. The light grey iron has a 
limit of elasticity at near one-half the maximum reached by the white 
iron, without any sign of reaching the limit of its elasticity. The grey 
has more ductility than the white iron, but has only about two-thirds 
the resilience of the latter. The dark grey irons are evidently better 
than either of the lighter grades, except in power of carrying an abso- 
lutely static load. The actual stretch of the outer surface particles is 
very nearly the same in all three. They are excellent specimens of their 
class, and considerably better than ordinarv iron-. 



* Reports of British Association; also Civil Engineer and Architects' Journal. 



26 



No. 37 is a " nialleableized cast-iron, " made from the extraordinary 
metal illustrated in No. 30. The process of malleableizing consists in 
decarbonization by heating the casting made from good white iron, in 
contact with iron oxide or other decarbonizing material. "Without re- 
moving any other constituent than the carbon, it produces a crude steel 
or an impure wrought-iron. When performed in the usual manner, 
melting the cast-iron in a cupola in contact with the fuel, and with some 
flux, and then carrying the process of malleableizing to the usual ex- 
tent, a metal is obtained such as is illustrated by the diagram marked 37. 
It retains the strength of the cast-iron, and acquires some ductility. 

No. 30 yielded 7° before fracture, while Xo. 37, vastly more ductile 
and resilient, only broke after a torsion of 39°, and a maximum elon- 
gation of 2 per cent. Taking the precaution to melt the iron in an " air 
furnace" — a form of " reverberatory " — and conducting the process of 
malleableizing more carefully, a still more valuable material was ob- 
tained. 

No. 35 represents this iron. Its resemblance to wrought-iron, both 
in appearance of fracture and in its strength and ductility, are greatly 
increased. It has a high limit of elasticity — over 20,000 pounds per 
square inch — and such ductility that it only breaks after a torsion of 
nearly 168°, and an elongation of " fibre" of 0.35. It is not very homo- 
geneous, but it is as strong, and almost as tough, as a good wrought-iron. 
This material has especial value for many purposes, because of the facility 
with which awkwardly shaped pieces can be made of it. In many cases, 
it will prove as good as wrought-iron and far cheaper. 

Fig. 11. Fig. 11 shows the appearance of this last 

specimen. Its resemblance to wrought iron is 
very noticeable. 




The lines running like the 



thread of a screw 
around the exterior of 
the neck, and the 
smooth even fracture 
in a plane precisely 
perpendicular to the 
axis, are the instruc- 
tive features. Fig. 
12, representing Xo. 33, is a specimen similar 
in character to Xo. 37. The comparative lack of 
ductility, its less regular structure, and its less 
perfect transformation are perfectly exhibited 



Fig. 12. 




Fig. 13 is an excellent 



'27 





cut of the white iron as east and withoui malleableizing. Its sur- 
Fig. 13. face where fractured, has flic general appear- 

ance of broken tool steel. The color and tex- 
ture of the metal are distinctive, however. It 
lias none of the " steely grain." Fig. 14 
represents the dark Fig. 14. 

grey iron. Its color, 
its granular structure 
and coarse grain are 
markedly character- 
istic and no one can 
fail to perceive, in the 
specimen, the general 
character which is ex- 
actly given by the autographic diagrams of the 
testing machine. 

10. Other Metals. — The diagrams num- 
bered 87, 88 and 89, are those of copper, tin 
and zinc. These specimens are all of cast metal, carefully selected under 
the direction of the writer and moulded and cast at the Stevens Institute 
of Technology. They exhibit neatly the wonderful superiority which 
the various kinds of iron and steel possess over the other useful metals. 
These metals all take a set under very small strains, pass their limits of 
elasticity at some indeterminable, but evidently low point, and possess 
very slight tenacity. 

Zinc, No. 89, by the regularity of its curve shows a very uniform 
structure. It increases very gradually in resistance to torsion, until it 
reaches the angle 50°, at which point it has a moment of torsional resist- 
ance of 36 foot-pounds, and a maximum tenacity of about 10,800 pounds 
per square inch. It loses its power of resistance, after rnpture com- 
mences, as regularly, but not as slowly, as it acquired it, and rupture be- 
comes complete at 63°. Its resistance is exceedingly small, and it is evi- 
dently unfit to bear either static or dynamic force. Its stretching power 
has a maximum of 0.04. 

Tin, No. 88, is equally remarkable for its exceedingly feeble resistance 
and its great ductility. The specimen was excellent, both in quality of 
metal and in closeness of structure, as was indicated by the clearness of 
the "tin cry" heard while undergoing the test and by the fine, smooth, 
clean fracture. The character of the curve is similar to that of zinc, but 
has far greater extent. Its elastic limit is quite indeterminable. The- 



28 

outline of the diagram indicates very perfect hornogeneousness. The 
maximum resistance to torsion is found at 240°, and under a stress of 19 
foot-pounds. Its tenacity deduced from the diagram is, at most, but 
5,700 pounds per square inch. Kupture occurs very gradually, and the 
piece separated entirely at 355°. Notwithstanding its great ductility, its 
low tenacity produces a low resilience, although in this quality it excels 
zinc, which latter metal had nearly double its strength. Its elongation by 
tension would have reduced its section to 0. 6 of the original cross area, 
if that reduction were proportional to the ductility shown by the diagram. 

Copper, No. 87, cast in green sand, like the zinc and tin just described, 
was found, on examination of the fracture, to differ from them in being 
exceedingly porous. The effect of this fault has been to weaken it 
seriously. Its curve closely resembles that of zinc, but is abruptly ter- 
minated by the piece suddenly breaking off at 46°. It reaches a maxi- 
mum sooner than zinc, at 29°, and its greatest resistance to torsion is 36 
foot-pounds, or to tension 10,800 pounds per square inch, precisely the 
same as zinc. Its ductility has a value of one and a half per cent. Its 
resilience is somewhat less than that of zinc. Its limit of elasticity is 
difficult to determine, but has been taken at 1\° where the moment of 
resistance is 13 foot-pounds, equivalent very nearly to 3,900 pounds 
tenacity, per square inch. 

No. 134 is the curve of cast copper, precisely similar to No. 87, but cast 
in a dry sand mould. The marked difference between these specimens is 
probably due, not only to the difference in degree of porosity which 
arises from the presence of vapor, which permeates the casting in one 
case, filling it with bubble holes, and Avhich is almost unobservable in the 
last, but the slower cooling of the dry sand casting also probably pro- 
duces its effect in strengthening the metal. This last specimen has a 
limit of elasticity at not far from 13|°, and under a torsional stress 
equivalent to a tension of 5,400 pounds per square inch. The maximum 
values of these quantities are found at 21°, and are 42 foot-pounds, and 
12,600 pounds per square inch respectively. The resilience of the sjjeci- 
men is much greater than that of the preceding, and its maximum elonga- 
tion is .026. Altogether, this is far better than the preceding, and it 
would seem that copper, and probably all its alloys, should, when possi- 
ble, be cast in dry sand, to secure density and strength. 

No. 141 is a piece of forged copper, hammered into a one-inch square 
bar, from a piece originally 3| inches wide and f inch thick. The most 
striking property noticed is its immense ductility, far exceeding that of 
any other piece of metal yet tested, and, in amount, many times as great 



29 

as the oasl metal. Its limit of elasticity is reached very quickly, although 

it is impossible to say precisely where it occurs. Comparing its •• elastic 

line " with the initial portion of the curve, it is seen that the slightest force 
produce's a set which is proportionally large as compared with the sets of 
other metals. The curverises very regularly and gradually to a m aximum , 
which is only attained, however, after a total angle of tension of 450 \ and 
which measures 96 foot-pounds moment, or 28,800 pounds per square 
inch. Rupture is finally obtained after a torsion of 543°. The maximum 
elongation is 210 per cent., the most elongated lines of particles being 
finally left of 3.100 times their original length. Hal this change of form 
occurred by reduction of section, the fractured area would have been but 
.323 the area of original section. The resilience of this piece of metal is 
evidently insignificant within the limit of which it would be seriously dis- 
torted by a blow, but is quite large in amount where resistance extends 
to the point of rupture. This is perfectly consonant with that knowledge 
of the material which every mechanic derives from experience with it. 
Here, however, we have a complete account of its properties, written out 
by the material itself with definite and accurate measures. 

11. General Conclusions. — These plates, exhibiting the diagrams, 
which are the autographs of all the useful metals, illustrate sufficiently 
well the remarkable fullness and accuracy with, which, their properties 
may be graphically represented, and the convenience with which they 
may be studied, with the aid of so simple a recording machine. A com- 
parison of results deduced as shown, with those obtained, so far as they 
can be obtained at all, the usual method of simply pulling the specimens 
asunder, and trusting to, sometimes, unskillful hands and an untrained 
observer, for the adjustment of weights and the registry of results, will 
indicate the close approximation of this method in even ascertaining the 
behavior of the metal in tension. On examining the beautifully plotted 
curves given by Knut StyfTe, as representing the results of the experi- 
ments, made by him and by his colleagues, with a tensile machine, no 
one can fail to be struck with, the similarity of those diagrams to the 
curves here produced automatically, and it will be readily believed that 
not only must there be very perfect correspondence of results where the 
two methods are carefully compared, but, also, that any theory of rup- 
ture must be defective which does not apply to both cases. The equa- 
tions of the curves here given and those of the curves obtained by Styffe 
must have forms as similar as the curves themselves. 

The constant ratio here assumed between the torsional resistance and 



30 

the tensile strength of the metals, and of homogeneous materials generally 
is based upon a comparison of the results here given with those obtained 
from the irons by tensile test, by the writer, and is confirmed by a com- 
pilation of results given by other experiments on the same brands. 

12. Testing within the limtt oe Elasticity. — In determining the 
value of materials of construction, it is usually more necessary to deter- 
mine the position of the limit of elasticity and the behavior of the metal 
within that limit than to ascertain ultimate strength or except, perhaps, 
for machinery, even the resilience. It is becoming well recognized by 
engineers who are known to stand highest in the profession, that it 
should be possible to test every piece of material which goes into an 
important structure and to then use it with confidence that it has been 
absolutely proven to be capable of carrying its load with a sufficient and 
known margin of safety. It has quite recently become a common prac- 
tice to test rods to a limit of strain determined by specification, and to 
compel their rejection when found to take a considerable permanent set 
under that strain. The method here described allows of this practice 
with perfect safety. The limit of elasticity occurs within the first 
two or three degrees, and, as seen, the specimen may be twisted a 
hundred, or even sometimes two hundred times as far without even 
reaching its maximum of resistance, and often far more than this before 
actual fracture commences. It is perfectly safe, therefore, to test, for ex- 
ample, a bridge rod up to the elastic limit, and then to place the rod in 
the structure, with a certainty that its capacity for bearing strain with- 
out injury has been determined and that formerly existing internal 
strain has been relieved. The autographic record of the test would be 
filed away, and could, at any time, be produced in court and submitted 
as evidence — like the " indicator card " of a steam engine — should any 
question arise as to the liability of the builder for any subsequent 
accident, or as to the good faith displayed in fulfilling the terms of his 
contract. A special machine has been designed for this case. 

13. The above will be sufficient to show the use and the value of this 
method. In the course of experiment upon a large number of specimens 
of all kinds of useful metals and of alloys, a number of interesting and 
instructive researches have been pursued, and some unexpected dis- 
coveries have been made. Before taking up the theory of rupture, the 
construction of equations, and the determination of their constants, a 
section will be devoted to an account of these investigations. 



AUTC 



WOODS 




PLATE I. 
AUTOGRAPHIC STRAIN-DIAGRAMS OF WOODS 

TESTING MACHINE OF PROFESSOR R. H. THURSTON. 




RAMS 



.. H. THURS 











PLATE It. 
AUTOGEAPHIC 8TRAIN-DIAGEAMS OF M E T A. L S 



TESTING MACHINE OF PROFESSOR R. H. THURSTON 



Torsional Moments. 
Foot-Pounds.)™ ^™- 




LIBRARY OF CONGRESS # 

028 116 609 8 



LIBRARY OF CONGRESS 

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Hollinger Corp. 
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